Automatic Integration of Functional Differential Equations: An Approach

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Automatic Integration of Functional Differential Equations: An Approach

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 1 , Issue 4 (December 1975) table of contents

Pages: 357 - 368

Year of Publication: 1975

ISSN:0098-3500

Author

Kenneth W. Neves

Babcock & Wilcox Co, P.O. Box 1260, Lynchburg, VA

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 45, Citation Count: 6

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	CHRISTIANSEN, J. Numerical solution of ordinary s~multaneous d~fferentml equatmns of the first order using a method of step changes Numer. Math., 14, 4 (1970), 317-324 Erratum, Numer. Math. 15, 1 (1970).
	2	Samuel Daniel Conte , Carl W. De Boor, Elementary Numerical Analysis: An Algorithmic Approach, McGraw-Hill Higher Education, 1980
	3	CRIER, C.W. Numerical methods for functional differential equations. In Delay D,fferent~al Eq~atzons and Their A pphcatwns, K Schmltt, Ed., Academic Press, New York, 1972, pp. i7-102.
	4	ELDSTEIN, A. Discretizatlon methods for retarded ordinary differential equations. Doctoral Dlss, U. of Cahforma, Los Angeles, 1964.
	5	FELDSTEIN, A, AND NEVES, K W High order methods for state dependent delay differential equations with non-smooth solutions. Presented at the SIAM Nat. Meeting, Hampton, Va., June 1973, Chronicle, SIAM Re~,., 16, 1 (1974), 134.
	6	FELDSTEIN, A, AND SOPKA, J. Numerical methods for nonhnear Volterra lntegro-dlffe~entml equatmns. To appear.{
	7	C. William Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall PTR, Upper Saddle River, NJ, 1971
	8	LAPIDUS, L, AND SEINFELD, J. Numerwal Solt~tzon of Ordinary Dzfferentzal Equatwns. Academic Press, New York, 197i.
	9	Kenneth W. Neves, Algorithm 497: Automatic Integration of Functional Differential Equations [D2], ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.369-371, Dec. 1975 [doi>10.1145/355656.355662]
	10	NEVES, K.W. Numerical solution of functional differential equations with state dependent lags. Doctoral Diss., Arizona State U., Tempe, Ariz., Oct. 1973.
	11	NEVES, K.W., AND FELDSTEIN, A. Characterization of jump discontinuities for state dependent delay d~fferentml equations. Presented at the SIAM Nat. Meeting, Hampton, Va., June 1973, also J. Math. Anal. and Appl., to appear.
	12	SCHMITT, K, Ed. Delay and Functwnal D~fferent, al Equatwns and Their Apphcations. Academm Press, New York, 1972.
	13	TAVERNINI, L. One step methods for the numerical solution of Volterra-functlonal differential equations. SIAM J. Numer. Anal. 8, 4 (1971), 786-795.
	14	User's Manual, IMSL Library 3, Edltmn 3, Vol. 1. International Mathematical and Statistical Libraries, Inc., Houston, Tex., 1974, pp. D-l, D-2.

CITED BY 6

	Kenneth W. Neves, Algorithm 497: Automatic Integration of Functional Differential Equations [D2], ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.369-371, Dec. 1975
	Kenneth W. Neves, Control of Interpolatory Error in Retarded Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.7 n.4, p.421-444, Dec. 1981
	Christopher T. H. Baker , Christopher A. H. Paul, Discontinuous solutions of neutral delay differential equations, Applied Numerical Mathematics, v.56 n.3, p.284-304, March 2006
	Alan Feldstein , Kenneth W. Neves , Skip Thompson, Sharpness results for state dependent delay differential equations: an overview, Applied Numerical Mathematics, v.56 n.3, p.472-487, March 2006
	S. M. Mahmoud, A class of three-point spline collocation methods for solving delay differential equations, International Journal of Computer Mathematics, v.84 n.10, p.1495-1508, October 2007
	Z. Bartoszewski , Z. Jackiewicz, Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations, Journal of Computational and Applied Mathematics, v.220 n.1-2, p.257-270, October, 2008